We also see concerning the other powers of the DO, e.g. the unnatural weather, bubbles of evil, spoiling food, etc., that the DO has equal power about all of the Westlands. Nothing suggests that it's worse in the Borderlands than in Tear, for example. The DO just has more power about the Blight, especially SG and the Pit, because it is apart from the normal universe and one can sense the Bore better there.

Nothing suggests that especially the DO's most prominent power, namely him being the "Lord of the Graves" and granting "immortality", would gradually decrease with the distance to SG. We also never hear anyone of the Forsaken in the far south of the Westlands or Semirhage in Seanchan muse that the DO will have a harder time, or even not be able to transmigrate them, there. On the contrary, the Forsaken obviously take it for granted that the DO can transmigrate them everywhere, except if balefire is involved (they also don't mention the theoretical very small amount exception). As far as we know even Lanfear, who apparently died in Finnland, could be transmigrated.